Buch, Englisch, Band 21, 284 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 615 g
Reihe: Cambridge Monographs on Applied and Computational Mathematics
Buch, Englisch, Band 21, 284 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 615 g
Reihe: Cambridge Monographs on Applied and Computational Mathematics
ISBN: 978-0-521-79211-0
Verlag: Cambridge University Press
Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Introduction; 1. From local to global approximation; 2. Trigonometric polynomial approximation; 3. Fourier spectral methods; 4. Orthogonal polynomials; 5. Polynomial expansions; 6. Polynomial approximations theory for smooth functions; 7. Polynomial spectral methods; 8. Stability of polynomial spectral methods; 9. Spectral methods for non-smooth problems; 10. Discrete stability and time integration; 11. Computational aspects; 12. Spectral methods on general grids; Bibliography.
